A
bstract
We analyse the Weak Gravity Conjecture for chiral four-dimensional F-theory compactifications with
N
= 1 supersymmetry. Extending our previous work on nearly tensionless heterotic strings ...in six dimensions, we show that under certain assumptions a tower of asymptotically massless states arises in the limit of vanishing coupling of a U(1) gauge symmetry coupled to gravity. This tower contains super-extremal states whose charge-to-mass ratios are larger than those of certain extremal dilatonic Reissner-Nordström black holes, precisely as required by the Weak Gravity Conjecture. Unlike in six dimensions, the tower of super-extremal states does not always populate a charge sub-lattice.
The main tool for our analysis is the elliptic genus of the emergent heterotic string in the chiral
N
= 1 supersymmetric effective theories. This also governs situations where the heterotic string is non-perturbative. We show how it can be computed in terms of BPS invariants on elliptic four-folds, by making use of various dualities and mirror symmetry. Compared to six dimensions, the geometry of the relevant elliptically fibered four-folds is substantially richer than that of the three-folds, and we classify the possibilities for obtaining critical, nearly tensionless heterotic strings. We find that the (quasi-)modular properties of the elliptic genus crucially depend on the choice of flux background. Our general results are illustrated in a detailed example.
The worldsheet dual of the symmetric product CFT Eberhardt, Lorenz; Gaberdiel, Matthias R.; Gopakumar, Rajesh
The journal of high energy physics,
04/2019, Letnik:
2019, Številka:
4
Journal Article
Recenzirano
Odprti dostop
A
bstract
Superstring theory on
AdS
3
×
S
3
×
T
4
with the smallest amount of NS-NS flux (“
k
= 1”) is shown to be dual to the spacetime CFT given by the large
N
limit of the free symmetric product ...orbifold Sym
N
T
4
. To define the worldsheet theory at
k
= 1, we employ the hybrid formalism in which the AdS
3
× S
3
part is described by the
p
s
u
1
,
1
|
2
1
WZW model (which is well defined). Unlike the case for
k
≥ 2, it turns out that the string spectrum at
k
= 1 does
not
exhibit the long string continuum, and perfectly matches with the large
N
limit of the symmetric product. We also demonstrate that the fusion rules of the symmetric orbifold are reproduced from the worldsheet perspective. Our proposal therefore affords a tractable worldsheet description of a tensionless limit in string theory, for which the dual CFT is also explicitly known.
A
bstract
We test various conjectures about quantum gravity for six-dimensional string compactifications in the framework of F-theory. Starting with a gauge theory coupled to gravity, we analyze the ...limit in Kähler moduli space where the gauge coupling tends to zero while gravity is kept dynamical. We show that such a limit must be located at infinite distance in the moduli space. As expected, the low-energy effective theory breaks down in this limit due to a tower of charged particles becoming massless. These are the excitations of an asymptotically tensionless string, which is shown to coincide with a critical heterotic string compactified to six dimensions.
For a more quantitative analysis, we focus on a U(1) gauge symmetry and use a chain of dualities and mirror symmetry to determine the elliptic genus of the nearly tensionless string, which is given in terms of certain meromorphic weak Jacobi forms. Their modular properties in turn allow us to determine the charge-to-mass ratios of certain string excitations near the tensionless limit. We then provide evidence that the tower of asymptotically massless charged states satisfies the (sub-)Lattice Weak Gravity Conjecture, the Completeness Conjecture, and the Swampland Distance Conjecture. Quite remarkably, we find that the number theoretic properties of the elliptic genus conspire with the balance of gravitational and scalar forces of extremal black holes, such as to produce a narrowly tuned charge spectrum of superextremal states. As a byproduct, we show how to compute elliptic genera of both critical and non-critical strings, when refined by Mordell-Weil U(1) symmetries in F-theory.
Hans Bethe sagte 1931 in einer fundamentalen Arbeit die Existenz von stark gebundenen Zuständen von Quasiteilchen voraus. Nun konnte eine internationale Kooperation erstmals derartige Bethe‐Strings ...in einem Kristall nachweisen.
Metastring theory and modular space-time Freidel, Laurent; Leigh, Robert G.; Minic, Djordje
The journal of high energy physics,
06/2015, Letnik:
2015, Številka:
6
Journal Article
Recenzirano
Odprti dostop
A
bstract
String theory is canonically accompanied with a space-time interpretation which determines S-matrix-like observables, and connects to the standard physics at low energies in the guise of ...local effective field theory. Recently, we have introduced a reformulation of string theory which does not rely on an a priori space-time interpretation or a pre-assumption of locality. This
metastring theory
is formulated in such a way that stringy symmetries (such as T-duality) are realized linearly. In this paper, we study metastring theory on a flat background and develop a variety of technical and interpretational ideas. These include a formulation of the moduli space of Lorentzian worldsheets, a careful study of the symplectic structure and consequently consistent closed and open boundary conditions, and the string spectrum and operator algebra. What emerges from these studies is a new quantum notion of space-time that we refer to as a quantum Lagrangian or equivalently a
modular space-time
. This concept embodies the standard tenets of quantum theory and implements in a precise way a notion of relative locality. The usual string backgrounds (non-compact space-time along with some toroidally compactified spatial directions) are obtained from modular space-time by a limiting procedure that can be thought of as a correspondence limit.
A
bstract
We examine the question how string theory achieves a sum over bulk geometries with fixed asymptotic boundary conditions. We discuss this problem with the help of the tensionless string on
ℳ
...3
×
S
3
×
T
4
(with one unit of NS-NS flux) that was recently understood to be dual to the symmetric orbifold Sym
N
(
T
4
). We strengthen the analysis of
1
and show that the perturbative string partition function around a fixed bulk background already includes a sum over semi-classical geometries and large stringy corrections can be interpreted as various semi-classical geometries. We argue in particular that the string partition function on a Euclidean wormhole geometry factorizes completely into factors associated to the two boundaries of spacetime. Central to this is the remarkable property of the moduli space integral of string theory to localize on covering spaces of the conformal boundary of ℳ
3
. We also emphasize the fact that string perturbation theory computes the grand canonical partition function of the family of theories ⊕
N
Sym
N
(
T
4
). The boundary partition function is naturally expressed as a sum over winding worldsheets, each of which we interpret as a ‘stringy geometry’. We argue that the semi-classical bulk geometry can be understood as a condensate of such stringy geometries. We also briefly discuss the effect of ensemble averaging over the Narain moduli space of
T
4
and of deforming away from the orbifold by the marginal deformation.
A
bstract
We systematically analyse weak coupling limits for 2-form tensor fields in the presence of gravity. Such limits are significant for testing various versions of the Weak Gravity and ...Swampland Distance Conjectures, and more broadly, the phenomenon of emergence. The weak coupling limits for 2-forms correspond to certain infinite-distance limits in the moduli space of string compactifications, where asymptotically tensionless, solitonic strings arise. These strings are identified as weakly coupled fundamental strings in a dual frame, which makes the idea of emergence manifest. Concretely we first consider weakly coupled tensor fields in six-dimensional compactifications of F-theory, where the arising tensionless strings play the role of dual weakly coupled heterotic strings. As the main part of this work, we consider certain infinite distance limits of Type IIB strings on K3 surfaces, for which we show that the asymptotically tensionless strings describe dual fundamental Type IIB strings, again on K3 surfaces. By contrast the analogous weak coupling limits of M-theory compactifications are found to correspond to an F-theory limit where an extra dimension emerges rather than tensionless strings. We comment on extensions of our findings to four-dimensional compactifications.
A
bstract
We demonstrate that all rigidly rotating strings with center of mass at the origin of the dS
3
static patch satisfy the Higuchi bound. This extends the observation of Noumi et al. for the ...open GKP-like string to all solutions of the Larsen-Sanchez class. We argue that strings violating the bound end up expanding towards the horizon and provide a numerical example. Adding point masses to the open string only increases the mass/spin ratio. For segmented strings, we write the conserved quantities, invariant under Gubser’s algebraic evolution equation, in terms of discrete lightcone coordinates describing kink collisions. Randomly generated strings are found to have a tendency to escape through the horizon that is mostly determined by their energy. For rapidly rotating segmented strings with mass/spin
<
1, the kink collisions eventually become causally disconnected. Finally we consider the scenario of cosmic strings captured by a black hole in dS and find that horizon friction can make the strings longer.
A
bstract
Superstring field theory expresses the perturbative S-matrix of superstring theory as a sum of Feynman diagrams each of which is manifestly free from ultraviolet divergences. The ...interaction vertices fall off exponentially for large space-like external momenta making the ultraviolet finiteness property manifest, but blow up exponentially for large time-like external momenta making it impossible to take the integration contours for loop energies to lie along the real axis. This forces us to carry out the integrals over the loop energies by choosing appropriate contours in the complex plane whose ends go to infinity along the imaginary axis but which take complicated form in the interior navigating around the various poles of the propagators. We consider the general class of quantum field theories with this property and prove Cutkosky rules for the amplitudes to all orders in perturbation theory. Besides having applications to string field theory, these results also give an alternative derivation of Cutkosky rules in ordinary quantum field theories.
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